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<p><dfn class="terminology">Theorem</dfn> If <span class="process-math">\(p(x)\text{,}\)</span> <span class="process-math">\(q(x)\)</span> and <span class="process-math">\(g(x)\)</span> are continuous in an open interval <span class="process-math">\(I\text{:}\)</span> <span class="process-math">\(\alpha&lt;x&lt;\beta\text{,}\)</span> which contains <span class="process-math">\(x_0\text{,}\)</span> then the initial value problem has a unique solution which is valid in <span class="process-math">\(I\text{.}\)</span></p>
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